And the Washington press was so disinterested in the idea that Boehner wasn’t asked about the tax during two press conferences he held to discuss the budget. A Boehner spokesman said House Republicans are so opposed to new spending programs that it doesn’t matter how Obama proposes to fund them.

A spokeswoman for Rep. Dave Camp (R-Mich.), the chairman of the House Ways and Means Committee who is also among tobacco companies’ top 2012 campaign recipients, wouldn’t even address the proposal specifically.

“The chairman is not interested in one-off tax hikes that fuel more deficit spending,” the spokeswoman said. “Instead, he is focused on comprehensive reform where everything is on the table.”

Sen. Frank Lautenberg (D-N.J.) and three Democratic co-sponsors have introduced legislation to increase taxes 93 percent on all tobacco products. The bill was referred to the Finance Committee, where it has yet to get a hearing.

Anti-smoking advocates generally have high praise for Obama, thanks to 2009 legislation he signed that increased the per-pack federal cigarette tax from 39 cents to $1.01 and gave the Food and Drug Administration authority to regulate tobacco products.

But his new proposal remains short of a Bush administration idea to make the tax $2.39 per pack. That suggestion, by a Health and Human Services committee in 2003, would have set the federal tax at $2.39 per pack by 2005, with the revenue earmarked to fund an array of anti-smoking campaigns.

As for Obama’s, the moment may have already passed for anything to happen with it, even if the White House changes course and decides to prioritize a push. Hansen, of the Cancer Society’s political arm, said the lack of coordination limited any ability to build a broad-based campaign of support.

But that’s not how the White House approached the effort.

“We saw it,” Hansen said, “when you saw it.”

Tarini Parti contributed to this report.

CORRECTION: An earlier version of this story misstated the timing and extent of the effort undertaken by the Cancer Action Network to support the cigarette tax proposal. It launched a Congressional lobbying effort and grassroots campaign in the days after the budget’s release.